at Google ScholarTitle data
Chubenko, Vladimir ; Kurz, Sascha:
Divisible minimal codes.
In: Serdica Journal of Computing.
Vol. 18
(2024)
Issue 2
.
- pp. 97-124.
ISSN 1312-6555
Abstract in another language
Minimal codes are linear codes where all non-zero codewords are minimal, i.e., whose support is not properly contained in the support of another codeword. The minimum possible length of such a k-dimensional linear code over GF(q) is denoted by m(k, q). Here we determine m(7, 2), m(8, 2), and
m(9, 2), as well as full classifications of all codes attaining m(k, 2) for k at most 7 and those attaining m(9, 2). We give improved upper bounds for m(k, 2) for
all dimensions k between 10 and 17. It turns out that in many cases the attaining extremal codes have the property that the weights of all codewords are divisible by some
constant ∆ > 1. So, here we study the minimum lengths of minimal codes where we additionally assume that the weights of the codewords are divisible by ∆. As a byproduct we also give a few binary linear codes improving the best known lower bound for the minimum distance.
Further data
| Item Type: | Article in a journal |
|---|---|
| Refereed: | Yes |
| Keywords: | minimal codes; divisible codes; optimal codes; quasi-cyclic codes;
acute sets |
| Subject classification: | Mathematics Subject Classification 2020: 94B05 (51E23) |
| Institutions of the University: | Faculties > Faculty of Mathematics, Physics und Computer Science Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics Faculties > Faculty of Mathematics, Physics und Computer Science > Department of Mathematics > Chair Mathematical Economics Faculties |
| Result of work at the UBT: | Yes |
| DDC Subjects: | 000 Computer Science, information, general works > 004 Computer science 500 Science > 510 Mathematics |
| Date Deposited: | 24 Jun 2025 11:34 |
| Last Modified: | 06 Oct 2025 12:07 |
| URI: | https://eref.uni-bayreuth.de/id/eprint/93969 |